Foreign Minister Ahmed Aboul Gheit has identified the detainee as Saud bin Salman bin Saud Al Thani, who he said flew out of Egypt on 23 September, hours after losing control of his speeding car that overturned and slammed into a crowd sitting on a grassy median strip on Cairo's airport road.
Egypt's prosecutor-general, Maher Abdel Wahed, said on Sunday that he had applied for Al Thani to be extradited to Egypt to face trial, but Aboul Gheit said such a move would be unnecessary as Qatari authorities would try him properly.
It is not immediately known whether the detainee was related to Qatar's ruling Al Thani family. Qatari officials were not available for comment.
But Qatar's embassy said Al Thani carried a "special Qatari passport that gave him immunity" to leave Egypt shortly after the crash, which occurred on the wide highway leading to Cairo's international airport from the city centre, the Egyptian Foreign Ministry said in a statement.
Al Thani flew out of Egypt on an EgyptAir flight to the Saudi city of Jedda before Egyptian authorities could issue orders preventing him from leaving, Abdel Wahed said.
On Friday, Egypt's Foreign Ministry summoned Qatar's charge d'affaires, Mohammed Ali al-Maliki, over the incident, but the envoy said his embassy had no knowledge of Al Thani's whereabouts and assured Egyptian authorities that the car did not belong to the Qatari diplomatic mission.